Monday, May 25, 2015

One of the goals of the HEAT project is to better understand the
hardness of the computational problems that underly SHE. One of those
problems, the Learning with Errors problem, has been investigated
repeatedly, but until now, there was no consistent way to specify
security parameters. In order to resolve this and increase interest in
LWE-based cryptosystems, we built an efficient online security estimation tool, available to anyone and straightforward to use.

The
LWE problem has three parameters: a dimension n, a Gaussian width
parameter s and a modulus q. In order to implement the complexity of
attacks against LWE as a function of these parameters, we combined
results from the literature of the last couple of years, with a main
focus on the Bounded Distance Decoding attack and the
Blum-Kalai-Wasserman (BKW) algorithm.

Our webtool implements the following three attacks:

-
The SIS-based attack is an attack against the LWE decision problem, as
described by Micciancio and Regev. Given a pair (A,t), one searches a
vector v orthogonal to the rows of A (mod q) and checks whether the
inner product <v,t> is small.

- The
Bounded distance decoding (BDD) attack is a combination of lattice basis
reduction and the nearest planes algorithm of Lindner and Peikert. It
attempts to solve the LWE search problem by searching a lattice point
close to t.

- The BKW (Blum-Kalai-Wasserman)
algorithm approaches the LWE search problem as a noisy linear system and
uses a blocked version of Gaussian elimination with back substitution.
This method was recently optimised by Duc, Tramèr and Vaudenay.

Designers
of cryptosystems are no longer restricted to parameters proposed in
papers, but can use this tool to query the security estimates of any set
of LWE parameters. Finally, in order to further simplify the process of
choosing LWE parameters, we also implemented the search for a suitable
modulus q. A user can input parameters n and s and a security level sec
to obtain the approximate value of log_2(q) that results in sec bits of
security.

Monday, May 4, 2015

Satellite Case Study for Homomorphic Encryption

The satellite industry is
strategically important for Europe, and generates significant revenue as well
as employing many tens of thousands of people in Europe. A particular issue
facing European satellite providers is shared use and reconfigurability of
infrastructure. Flexibility and configurability, and particularly shared use of
satellites and their infrastructure, is essential to enable affordable use of
satellites. The costs of launching and managing a single use satellite are
prohibitive for many organisations. The ability to share this cost over
multiple customers would expand the commercial reach of European satellite
providers.

Shared infrastructure would
ideally cover the satellites themselves, communication links to the ground, and
the ground infrastructure which collates, processes and otherwise manages data
received from the satellites. However, it brings with it security concerns due
to the differing commercial and national sensitivities of the applications and
data. In the HEAT project, we are looking at how Homomorphic Encryption could
allow encryption to be used to provide the required security separation on such
shared infrastructure, while still allowing essential and value-add processing
of data to take place. It could also allow more cost-effective outsourcing of
data processing and storage to Cloud Computing providers.

Potential
applications areas are:

Commercial domain: the ground segment for the European Space Agency
(ESA) Copernicus programme. Access to the Sentinel satellites’
Earth-observation data and generated products is restricted for commercial
reasons. These missions will require increased processing capacity and would
benefit from Cloud solutions.

Scientific domain: the future Euclid ground segment. Scientific data
for missions such as Euclid are confidential as access needs to be restricted
to institutes, universities, etc. contributing to the mission, in order to
ensure that they will publish the first papers and have the benefit of any discoveries.
The confidentiality of scientific data is not uniquely defined. Therefore,
solutions that allow flexibility in the security separation required (i.e. are
not tied to the infrastructure) and allow outsourcing of the processing and
storage would be of significant benefit.

For more than 40 years now,
Thales Alenia Space has designed, integrated, tested, operated and delivered
innovative space systems. Thales Alenia Space’s satellites and payloads are
recognized worldwide as benchmarks in delivering communications and navigation
services, monitoring our environment and the oceans, better understanding
climate change and supporting scientific research. Thales Alenia Space is a
leader in Earth observation, based on its high or very-high resolution optical
and radar payloads. The appropriate handling of such sensitive data, using
techniques such as homomorphic encryption, is a challenge, which the results of
the HEAT project will help to address.